I think they would definitely need to have it; it's the defining feature of the class, and gives the class its visual identity alongside the blindfolds, glaives and tattoos. Assuming that they might not always have those items, metamorphosis allows them to maintain their identity in the absence of their glaives or tattoos.

Warlocks canonically learned the skill by replicating Illidan's ability, so it'd be a little weird if Warlocks kept the ability but the class they learned it from lost it. They should both have the ability, though Demon Hunters should be more heavily build around it and have a different visual.